Oscillation criteria for first order linear delay differential equations with several variable delays

Garab, Ábel; Stavroulakis, I. P.

doi:10.1016/j.aml.2020.106366

Cited by 9 publications

(8 citation statements)

References 13 publications

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“…The conditions in the next theorem, established in [30], essentially improve related conditions in the literature.…”

Section: Oscillation Criteria For Equation (1)mentioning

confidence: 66%

“…where a : [t 1 , ∞) → R is a continuous function which tends to some finite limit as t → ∞, and b : [t 1 , ∞) → R is a continuously differentiable function for which lim t→∞ b (t) = 0 holds. For more information about slowly varying functions and their characterization the reader is referred to the papers [27][28][29][30] and the references cited therein. In a subsequent paper, Garab [29] studied the case of the differential equation with variable delay…”

Section: Oscillation Criteria For Equation (1)mentioning

confidence: 99%

“…Very recently Garab and Stavroulakis [30] considered the linear differential equation with several variable delays:…”

Section: Oscillation Criteria For Equation (1)mentioning

confidence: 99%

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A Survey on Sharp Oscillation Conditions of Differential Equations with Several Delays

et al. 2020

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This paper deals with the oscillation of the first-order differential equation with several delay arguments x′t+∑i=1mpitxτit=0,t≥t0, where the functions pi,τi∈Ct0,∞,R+, for every i=1,2,…,m,τit≤t for t≥t0 and limt→∞τit=∞. In this paper, the state-of-the-art on the sharp oscillation conditions are presented. In particular, several sufficient oscillation conditions are presented and it is shown that, under additional hypotheses dealing with slowly varying at infinity functions, some of the “liminf” oscillation conditions can be essentially improved replacing “liminf” by “limsup”. The importance of the slowly varying hypothesis and the essential improvement of the sufficient oscillation conditions are illustrated by examples.

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“…The conditions in the next theorem, established in [30], essentially improve related conditions in the literature.…”

Section: Oscillation Criteria For Equation (1)mentioning

confidence: 66%

Section: Oscillation Criteria For Equation (1)mentioning

confidence: 99%

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A Survey on Sharp Oscillation Conditions of Differential Equations with Several Delays

et al. 2020

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“…The qualitative properties of functional differential equations have attracted the attention of many researchers; see . In particular, the oscillation theory of Equation (1) has received increasing interest in recent years; see for example [1,2,[8][9][10]12,[16][17][18]. However, only a few works have considered the distance between zeros of Equation ( 1) and its general forms.…”

Section: Introductionmentioning

confidence: 99%

Upper Bounds for the Distance between Adjacent Zeros of First-Order Linear Differential Equations with Several Delays

Attia

Chatzarakis

2022

Mathematics

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The distance between successive zeros of all solutions of first-order differential equations with several delays is studied in this work. Many new estimations for the upper bound of the distance between zeros are obtained. Our results improve many-well known results in the literature. We also obtain some fundamental results for the lower bound of the distance between adjacent zeros. Some illustrative examples are introduced to show the accuracy and efficiency of the obtained results.

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“…It should be mentioned that the idea how to obtain sharp oscillation conditions in the continuous time case by considering slowly varying coefficients originated from Pituk [22]. Moreover, the continuous-time result has been recently generalized in [10] and in [12] for variable delay and several variable delays, respectively. The next work of the present authors is to study discrete analogues of these problems.…”

Section: Introductionmentioning

confidence: 99%

A sharp oscillation criterion for a difference equation with constant delay

2020

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It is known that all solutions of the difference equation $$\Delta x(n)+p(n)x(n-k)=0, \quad n\geq0, $$ Δ x ( n ) + p ( n ) x ( n − k ) = 0 , n ≥ 0 , where $\{p(n)\}_{n=0}^{\infty}$ { p ( n ) } n = 0 ∞ is a nonnegative sequence of reals and k is a natural number, oscillate if $\liminf_{n\rightarrow\infty}\sum_{i=n-k}^{n-1}p(i)> ( \frac {k}{k+1} ) ^{k+1}$ lim inf n → ∞ ∑ i = n − k n − 1 p ( i ) > ( k k + 1 ) k + 1 . In the case that $\sum_{i=n-k}^{n-1}p(i)$ ∑ i = n − k n − 1 p ( i ) is slowly varying at infinity, it is proved that the above result can be essentially improved by replacing the above condition with $\limsup_{n\rightarrow\infty}\sum_{i=n-k}^{n-1}p(i)> ( \frac{k}{k+1} ) ^{k+1}$ lim sup n → ∞ ∑ i = n − k n − 1 p ( i ) > ( k k + 1 ) k + 1 . An example illustrating the applicability and importance of the result is presented.

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Oscillation criteria for first order linear delay differential equations with several variable delays

Cited by 9 publications

References 13 publications

A Survey on Sharp Oscillation Conditions of Differential Equations with Several Delays

A Survey on Sharp Oscillation Conditions of Differential Equations with Several Delays

Upper Bounds for the Distance between Adjacent Zeros of First-Order Linear Differential Equations with Several Delays

A sharp oscillation criterion for a difference equation with constant delay

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